I'm aware that a teleconverter will reduce the amount of light reaching the film or sensor in a camera, and as such you hear people banding around things like "With a 2x teleconverter this 300mm f/2.8 becomes a 600mm f/5.6".

Given the aperture isn't physically any different, I wonder how that affects depth of field (and associated effects like bokeh). It would make sense that the depth of field remains the same, and the image is merely cropped.

Is it just another one of these things that people say, that may be convenient for exposure calculations, or is there actually a change in the image produced?

4 Answers
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TL;DR version: Teleconverters don't affect depth of field at any given distance. They literally transform your 300 f/2.8 lens into a 600 f/5.6 lens. Any 600 f/5.6 lens, teleconverted or not, will have the same depth of field as a 300 f/2.8 lens.

There's a lot of confusion about the relationship between depth of field, aperture, f-stop, and focal length. In reality, it's all very simple:

Depth of field is determined by focal distance and the apparent size of the front element of the lens.

By apparent diameter, I mean the width of the area of the front element that isn't blocked by the aperture.

You can actually see how big this apparent diameter is, by looking at the front of a lens while it's detached and the aperture is held open.

The relationship between f-stop, focal length, and apparent lens diameter is as follows:

(Size of aperture in mm) = (Focal length in mm) ÷ (f-stop)

For example:

The apparent diameter of a 210mm lens set to f/4.5 is 47mm,

The apparent diameter of a 70mm lens set to f/4.5 is 15.5mm,

The apparent diameter of a 70mm lens set to f/8 is 8.75mm,

And the apparent diameter of an 18mm lens set to f/3.5 is a paltry 5.1mm.

Now, back to depth of field. Depth of field is the distance in front of and behind the focused distance that is still "acceptably" in focus. Since the level of acceptable blur differs from person to person, a better way to analyze depth of field is through the circle of confusion.

Here's a handy picture from the Wikipedia page on Circle of Confusion:

The circle of confusion is the area on the sensor that is hit by light from a single point. If you're in front of or behind the plane of focus, then your circle of confusion gets bigger. At the plane of focus, the circle of confusion is (ideally, but never in practice) zero.

How quickly your circle of confusion grows as you move away from the plane of focus is a factor of one thing only: The angle between the widest converging lines (the edge of your apparent lens size). Now, this means a few things:

If you are focused 10 times further away, you have to go roughly 10 times further from the plane of focus to get the same change in your circle of confusion

Two lenses focused at the same distance, with the same apparent size, will result in the same change in your circle of confusion (and therefore the same depth of field.)

Conversely, this also debunks several commonly held beliefs about depth of field:

Two lenses at the same f-stop do not necessarily have the same depth of field. The longer lens will have a shorter depth of field, because it has a bigger apparent size. (Sorry, Matt.)

Teleconverters, cropping, and smaller sensors do not have any effect on depth of field at a given apparent size (f-stop and focal length).

Take two pictures: one with a 35mm f/1.8, and one with a 210mm f/11. Now, crop the 35mm image to have the same field of view as the other image. They will have almost exactly the same depth of field. Here you go:

Firstly, no need to apologise - I was talking about two lenses with the same focal length not two lenses with different focal lengths. Secondly your statement that a telecoverter doesn't affect depth of field could be a little misleading in this case as the question is "does a 300 f/2.8 with a 2x converter have the DOF of a 600 f/2.8 or a 600 f/5.6" so it does affect DOF in the sense that the relative aperture size changed.
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Matt GrumNov 17 '10 at 13:13

And the answer is that a 300 f/2.8 with a 2x converter acts EXACTLY like a 600 f/5.6 - in both light gathering ability and in depth of field.
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Evan KrallNov 17 '10 at 17:09

Excellent answer. Thanks for bringing CoC into the mix. It should be noted that CoC is affected by the imaging medium, which is why most DOF calculations involve the minimum CoC of the imaging medium in addition to focal length and aperture. This is not really a factor for reductions or direct prints at native resolution, but it is an important factor for enlargements. You can find formulas here: en.wikipedia.org/wiki/Depth_of_field (under DOF Formulas.)
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jrista♦Nov 17 '10 at 20:49

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It should also be noted that, according to Leslie D. Strobel, in his book "View camera technique", around page 150 or so, he provides strong evidence and some math indicating that cropping DOES affect the amount of DOF present in a final image. While physically DOF as projected by a lens does not change, the perception of the viewer of a final image should not be ignored when calculating DOF. Read more here: books.google.com/…
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jrista♦Nov 17 '10 at 20:55

By that logic, you get less depth of field by cropping an existing image?
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Rowland Shaw♦Nov 16 '10 at 19:05

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@Rowland - No. Cropping does not affect the angle at which light enters the lens because it does not increase focal-length. It is the same when mounting a lens on cameras with different sensor sizes, you get a 'cropped' field-of-view but you didn't change focal-length.
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ItaiNov 16 '10 at 19:42

But there is going to be the same field of view in the centre portion of a shot at 300mm compared to a 600mm lens
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Rowland Shaw♦Nov 16 '10 at 19:57

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@Rowland - Depth-of-field can be defined by aperture size and focal-length alone. How much you crop changes the field-of-view in the picture (not the lens') but has no effect on depth-of-field. If you need more explanations then I suggest you look up how depth-of-field works. Otherwise it may end up a very long discussion here :)
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ItaiNov 16 '10 at 20:10

Cropping does affect the apparent DOF, though. If you take a full-frame image that is mostly in-focus in the center, and blurred along the top and bottom edges, cropping WILL introduce a change in the dof that is apparent in the image (assuming the cropped version and FF version are scaled to the same size). Sensor does play a specific role in DOF calculations as well, from the standpoint of CoC. A smaller pixel allows for finer CoC, which affects DOF when enlarging for print. Most official DOF formulas take into account CoC (which is a function of imaging medium) as well length & aperture.
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jrista♦Nov 17 '10 at 20:39

Suppose that using a teleconverter extended the focal length and as a result let in less light but without affecting the depth of field. As well as making a 600 f/5.6 a manufacturer could take an existing a 300 f/2.8 design and incorporate some teleconverter optics but in the same body. They would then be able to offer two versions of the 600mm lens that behave exactly the same exposure wise but one would have the DOF of a 600 f/5.6 and one would have the DOF of a 600 f/2.8.

They could also replace the 300 f/2.8 with a 150 f/1.4 with incorporated telecoverter, and be able to offer 3 versions of the 600 with different DOF et cetera et cetera.

Eventually you arrive at a lens with infintesimally small depth of field but still behaving like a 5.6, which is clearly absurd, thus the original proposition (that the DOF is unchanged by a telecoverter) must be false.

Your assumptions are not purely theoretical. Real-life telephoto lenses have a negative group at the back that behaves much like a teleconverter.
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Edgar BonetNov 16 '10 at 15:04

yep, it behaves exactly like a telecoverter in fact, hence the name "tele" "converter", it allows a standard lens to have a focal length longer than the physical length which is the defining feature of a telephoto lens
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Matt GrumNov 16 '10 at 16:26

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Your argument is invalid, specifically "one would have the DOF of a 600 f/5.6 and one would have the DOF of a 600 f/2.8." In reality, one would have the DOF of a 600 f/5.6, and the other would have the DOF of a 300 f/2.8. Here's the secret: A 300 f/2.8 has the same depth of field as a 600 f/5.6, NOT a 600 f/2.8
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Evan KrallNov 17 '10 at 19:20

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@Evan Krall you seem to have missed the point of Reductio ad Absurdum, my point was that assume the premise then you have one lens with the DOF of a 600 f/2.8 and one lens with the DOF of a 600 f/5.6, as this is absurd Ye premise must be false. I'm in agreement with the other answers to this question!
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Matt GrumNov 17 '10 at 22:39

sorry guys but when i use a DOF calculator a 300mm f2.8 is not exactly like a 600mm f5.6. the number don´t match....
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user17481Mar 1 '13 at 11:56

Depth of field is determined by the focusing distance and physical aperture size (nicely explained by Evan Krall). Adding a teleconverter does not change the physical aperture size; you are simply magnifying the image already projected by the lens, and the focal length and f-number increase together in proportion.

Because the physical aperture size is unchanged, depth of field is unchanged for a given focusing distance.